Gathering Asynchronous Robots in a Tree Sruti Gan Chaudhuri - PowerPoint PPT Presentation

Gathering Asynchronous Robots in a Tree Sruti Gan Chaudhuri Jadavpur University, India GRASTA-MAC 2015 Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 1 / 27

Definition of the problem Given a tree Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 2 / 27

Definition of the problem Given a tree Randomly distributed mobile agents/robots ( autonomous, homogeneous, non distinguishable, silent ) in nodes Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 3 / 27

Definition of the problem Given a tree Randomly distributed mobile agents/robots ( autonomous, homogeneous, non distinguishable, silent ) in nodes The robots have to gather at a single node Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 4 / 27

Computational model Robots have no identity Nodes and edges of the graphs are not marked The robots have their local coordinate systems Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 5 / 27

Computational model LOOK Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 6 / 27

Computational model COMPUTE DESTINATION Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 7 / 27

Computational model MOVE Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 8 / 27

Computational model Oblivious: forget earlier computations. No multiplicity detection capabilities. Activation Schedule: Synchronous/Semi synchronous/Asynchronous Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 9 / 27

Motivation Results 1: Gathering in graph in general is not possible even with synchronicity. Ref: Gabriele Di Stefano, Alfredo Navarra, Optimal Gathering of Oblivious Robots in Anonymous Graphs , SIROCCO 2013, Volume 8179 of the series Lecture Notes in Computer Science pp 213-224. Results 2 Gathering in plane in general is not possible. (Ref: 1. Pierre Courtieu, Lionel Rieg, S´ ebastien Tixeuil, Xavier Urbain, Impossibility of gathering, a certification , Information Processing Letters, Volume 115, Issue 3, March 2015, Pages 447-45. 2. Paola Flocchini, Giuseppe Prencipe, Nicola Santoro, Distributed Computing by Oblivious Mobile Robots , Synthesis Lectures on Distributed Computing Theory August 2012, Chapter 3, pages 17 - 61.) Results 3 Gathering in plane is possible with agreement in coordinate axes even when the robots have limited visibility. Ref: Paola Flocchini, Giuseppe Prencipe, Nicola Santoro, Peter Widmayer, Gathering of asynchronous robots with limited visibility , Theoretical Computer Science, Volume 337, Issues 1–3, 9 June 2005, Pages 147-168, Results 4 Samuel Guilbault, Andrzej Pelc, Gathering asynchronous oblivious agents with local vision in regular bipartite graphs , Journal Theoretical Computer Science, Volume 509, October, 2013 Pages 86-96. Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 10 / 27

Some open questions Many results in gathering in grid, ring consider the knowledge of multiplicity detection. Can we remove this? All the results in continuous domain under Synchronous, Semi synchronous or Asynchronous model, do not hold in discrete domain. E.g., Gathering is possible under synchronous model in continuous domain but not in discrete domain. Whan happens in Limited visibility in general graph? Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 11 / 27

Gathering in tree under limited visibility No multiplicity detection Asynchronous Limited visibility Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 12 / 27

When destination is given Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 13 / 27

When destination is given Eliminate the peripheral nodes The robots only remember their parents Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 14 / 27

When destination is given Eliminate the peripheral nodes The robots only remember their parents Use pebbles 1 to mark path towards leaf 1Balasingham Balamohan, Stefan Dobrev, Paola Flocchini, and Nicola Santoro. Asynchronous exploration of an unknown anonymous dangerous graph with o (1) pebbles. In SIROCCO, pages 279–290. Springer, 2012. Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 15 / 27

Movement strategy for a robot If I see a robot in neighbor(which is not destination) node, I will not move Assured The robots will not toggle The robots will not be in deadlock: there always be a robot which will move unless it is already in destination. Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 16 / 27

When the destination is not given Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 17 / 27

When the robots are completely oblivious The graph (drawing) is oriented. Visibility graph of the robots is connected. Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 18 / 27

When the robots are completely oblivious The graph (drawing) is oriented. Visibility graph of the robots is connected. The robots gather to one of the corner most nodes, e.g., at down-right most node which has a robot. Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 19 / 27

Movement strategy for a robot If I see a robot in more than one neighboring nodes, I will not move. No Move Assured The visibility graph will not be disconnected. Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 20 / 27

Movement strategy for a robot If I see a robot in more than one neighboring nodes, I will not move. Else If I see a robot below my horizontal axis , I move to that node. Assured The visibility graph will not be disconnected. Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 21 / 27

Movement strategy for a robot If I see a robot in more than one neighboring nodes, I will not move. Else If I see a robot below my horizontal axis , I move to that node. OR If I see a robot right to my vertical axis, I move to that node. Assured The visibility graph will not be disconnected. The robots will move to the right-down most roots. Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 22 / 27

Gathering in tree under limited visibility Gathering in Tree Under Limitted Visibility Gathering node given The robots are not completely oblivious Gathering node not given The robots are completely oblivious The graph is oriented Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 23 / 27

Gathering in tree under limited visibility Gathering in Tree Under Limitted Visibility Gathering node given The robots are not completely oblivious Gathering node not given The robots are completely oblivious The graph is oriented True for Grids in many cases Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 24 / 27

On going development What happens if the Graph is not oriented? To explore the limited visibility model in general graph Optimizing the robots movement Collision avoidence algorithm Directed Graph (characterization) ... Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 25 / 27

Acknowledgement Krishnendu Mukhopadhyaya (Professor), ISI, Kolkata, India. Sumitro Bhawmik (Research Scholar), IIT Kharagpur, India. Srabani Mukhopadhyaya (Professor), BITM, Kolkata, India. Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 26 / 27

Thank You Sruti Gan Chaudhuri (Jadavpur University, India) Gathering Asynchronous Robots in a Tree GRASTA-MAC 2015 27 / 27